WITHDRAWN: Fast, Large-Scale Tetrahedral Mesh Generation on a Single GPU

A parallel Delaunay refinement algorithm on GPU by multi-round of parallel point insertion is proposed for large-scale tetrahedral mesh generation. It takes the CDT T of piecewise linear complex (PLC) as input and iteratively refine it by inserting points at the centroids of the tetrahedron in parallel until desired mesh size is met. In each iteration, the tetrahedron that do not meet the mesh size are first identified and are regarded as bad elements. Then, some or all of these bad tetrahedron are selected as starts for multi-round cavity growing, so as to obtain as many non-overlapping cavities as possible. And among these cavities, a further step is conducted to identify independent cavities for the purpose of refinement in parallel. After that, the independent cavities are repaired to make sure the elements after refinement are all valid. Finally, cavity reconstruction is executed in parallel the obtain the refined element of the cavities, and the mesh data is updated accordingly. Numerical results show that the proposed method is able to generate tetrahedral meshes with up to 450 million elements at a speed of over 18 million elements per second on a single 4090D (24G) GPU, and the quality of the generated meshes is very close to those generated on CPU in terms of the distribution of interior angles of tetrahedron.